{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 6. Decision Trees"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**在决策树中，最能区分类别的特征将作为最先判断的条件，然后依次向下判断各个次优特征**。决策树的核心就在于如何选取每个节点的最优判断条件，也即特征选择的过程。而在每一个判断节点，决策树都会遵循一套if-then的规则："
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "与SVM一样，决策树是多功能的机器学习算法，\n",
    "\n",
    "* 可以执行分类和回归任务，甚至是多输出任务。 \n",
    "* 它们是非常强大的算法，能够拟合复杂的数据集。例如，在第2章中，您在加州住房数据集上训练了一个DecisionTreeRegressor模型，使其完美拟合（实际上过拟合了）。\n",
    "* 决策树也是随机森林的基本组成部分（参见第7章），这是最强大的机器学习算法之一\n",
    "\n",
    "今天。在本章中，我们将\n",
    "* 首先讨论如何训练，可视化和使用决策树进行预测。\n",
    "* 然后我们将介绍Scikit-Learn使用的CART训练算法，我们将讨论如何规范树木并将其用于回归任务。 \n",
    "* 最后，我们将讨论决策树的一些局限性。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# To support both python 2 and python 3\n",
    "from __future__ import division, print_function, unicode_literals\n",
    "\n",
    "# Common imports\n",
    "import numpy as np\n",
    "import os\n",
    "\n",
    "# to make this notebook's output stable across runs\n",
    "np.random.seed(42)\n",
    "\n",
    "# To plot pretty figures\n",
    "%matplotlib inline\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['axes.labelsize'] = 14\n",
    "plt.rcParams['xtick.labelsize'] = 12\n",
    "plt.rcParams['ytick.labelsize'] = 12\n",
    "\n",
    "# Where to save the figures\n",
    "PROJECT_ROOT_DIR = \"F:\\ML\\Machine learning\\Hands-on machine learning with scikit-learn and tensorflow\"\n",
    "CHAPTER_ID = \"06_Decision Trees\"\n",
    "\n",
    "def image_path(fig_id):\n",
    "    return os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID, fig_id)\n",
    "\n",
    "def save_fig(fig_id, tight_layout=True):\n",
    "    print(\"Saving figure\", fig_id)\n",
    "    if tight_layout:\n",
    "        plt.tight_layout()\n",
    "    plt.savefig(image_path(fig_id) + \".png\", format='png', dpi=300)\n",
    "    \n",
    "    \n",
    "# Ignore useless warnings (see SciPy issue #5998)\n",
    "# 忽略无用警告\n",
    "import warnings\n",
    "warnings.filterwarnings(action=\"ignore\", message=\"^internal gelsd\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.1 Training and Visualizing a Decision Tree"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "要理解决策树，让我们构建一个决策树并查看它是如何进行预测。 以下代码在iris数据集上训练DecisionTreeClassifier（见第4章）："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DecisionTreeClassifier(class_weight=None, criterion='gini', max_depth=2,\n",
       "            max_features=None, max_leaf_nodes=None,\n",
       "            min_impurity_decrease=0.0, min_impurity_split=None,\n",
       "            min_samples_leaf=1, min_samples_split=2,\n",
       "            min_weight_fraction_leaf=0.0, presort=False, random_state=None,\n",
       "            splitter='best')"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "\n",
    "iris = load_iris()\n",
    "X = iris.data[:,2:] # petal length and width\n",
    "y = iris.target\n",
    "\n",
    "tree_clf = DecisionTreeClassifier(max_depth=2)\n",
    "tree_clf.fit(X,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "你可以通过使用**export_graphviz（）**方法输出名为**iris_tree.dot**的图形定义文件来可视化训练好的决策树："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.tree import export_graphviz\n",
    "\n",
    "export_graphviz(\n",
    "    tree_clf,\n",
    "    out_file=image_path(\"iris_tree.dot\"),\n",
    "    feature_names=iris.feature_names[2:],\n",
    "    class_names=iris.target_names,\n",
    "    rounded=True,\n",
    "    filled=True\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "然后，你可以使用graphviz包中的dot命令行工具将此**.dot**文件转换为各种格式，如PDF或PNG。下面这条命令行将.dot文件转换为.png图像文件：\n",
    "\n",
    "$ dot -Tpng iris_tree.dot -o iris_tree.png\n",
    "\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "windows下使用安装Graphviz:\n",
    "\n",
    "下载安装包：https://graphviz.gitlab.io/_pages/Download/Download_windows.html\n",
    "\n",
    "使用：\n",
    "\n",
    "https://www.cnblogs.com/shuodehaoa/p/8667045.html\n",
    "\n",
    "https://www.jianshu.com/p/6d9bbbbf38b1\n",
    "\n",
    "https://blog.csdn.net/lanchunhui/article/details/49472949\n",
    "\n",
    "https://blog.csdn.net/qq_41185868/article/details/79008351"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "下面的代码是把生成的iris_tree.png 显示出来，具体可以参考：[Jupyter Notebook插入图片的4种方法](https://blog.csdn.net/qq_33039859/article/details/78507316)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 14,
     "metadata": {
      "image/png": {
       "height": 400,
       "width": 400
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 你的第一个决策树长这样\n",
    "from IPython.display import Image\n",
    "Image(filename=\n",
    "      \"F:/ML/Machine learning/Hands-on machine learning with scikit-learn and tensorflow/images/06_Decision Trees/iris_tree.png\",\n",
    "      width=400,height=400,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.2 Making Predictions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "让我们看看图6-1(即上图)中表示的树是如何进行预测的。\n",
    "\n",
    "* 假设您找到了鸢尾花，并且您想对其进行分类。从根节点（深度0，顶部）开始：此节点询问**花瓣的长度是否小于2.45厘米**：\n",
    "    \n",
    "    * 如果是，则向下移动到根的左子节点（深度1，左）。在这种情况下，它是一个  叶子节点（即，它没有任何子节点），因此它不会问任何问题：您可以简单地查看该节点的预测类，并且决策树预测您的花是Iris-Setosa（ class = setosa）。\n",
    "\n",
    "\n",
    "* 现在假设你找到了另一朵花，但这次花瓣的长度大于2.45厘米。您必须向下移动到根的右子节点（深度1，右侧），即它不是一个叶子节点，所以它问另一个问题：**花瓣宽度是否小于1.75厘米**：\n",
    "    \n",
    "    * 如果是，那么你的花很可能是Iris-Versicolor（深度2，左）。\n",
    "    \n",
    "    * 如果没有，很可能是Iris-Virginica（深度2，右）。这真的很简单。\n",
    "\n",
    "决策树的许多特性之一是它们只需要很少的数据准备。特别是，它们**根本不需要特征缩放或居中**。"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. 节点的**samples**属性计算它适用的训练实例数。例如，100个训练实例的花瓣**长度**大于2.45厘米（深度1，右），其中54的花瓣**宽度**小于1.75厘米（深度2，左）。\n",
    "\n",
    "2. 节点的**value**属性告诉我们此节点适用于每个类的训练实例数：例如，右下角节点适用于0 Iris-Setosa，1 Iris-Versicolor和45 Iris-Virginica。\n",
    "\n",
    "3. 最后，节点的**gini**属性测量其**impurity**：如果节点应用的所有训练实例属于同一个类，则该节点为“纯”（gini = 0）。 例如，由于深度为 -1 的左节点仅适用于Iris-Setosa训练实例，因此它是纯粹的并且其**gini**评分为0。\n",
    "\n",
    "公式6-1显示了训练算法如何计算第i个节点的**gini**评分$G_i$。 例如，深度为2的左节点的**gini**评分等于\n",
    "\n",
    " $ 1 - (0/54)^2 - (49/54)^2 - (5/54)^2≈0.168$。 不久将讨论另一种**impurity measure**。\n",
    " ![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "其中，$p_{i,k}$是类别k实例的实例数，在第i个节点的所有训练实例中所占的比例。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure decision_tree_decision_boundaries_plot\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f8cbc75cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.colors import ListedColormap\n",
    "\n",
    "def plot_decision_boundary(clf, X, y, axes=[0, 7.5, 0, 3], iris=True, legend=False, plot_training=True):\n",
    "    x1s = np.linspace(axes[0], axes[1], 100)\n",
    "    x2s = np.linspace(axes[2], axes[3], 100)\n",
    "    x1, x2 = np.meshgrid(x1s, x2s)\n",
    "    X_new = np.c_[x1.ravel(), x2.ravel()]\n",
    "    y_pred = clf.predict(X_new).reshape(x1.shape)\n",
    "    custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n",
    "    plt.contourf(x1, x2, y_pred, alpha=0.3, cmap=custom_cmap)\n",
    "    if not iris:\n",
    "        custom_cmap2 = ListedColormap(['#7d7d58','#4c4c7f','#507d50'])\n",
    "        plt.contour(x1, x2, y_pred, cmap=custom_cmap2, alpha=0.8)\n",
    "    if plot_training:\n",
    "        plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"yo\", label=\"Iris-Setosa\")\n",
    "        plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bs\", label=\"Iris-Versicolor\")\n",
    "        plt.plot(X[:, 0][y==2], X[:, 1][y==2], \"g^\", label=\"Iris-Virginica\")\n",
    "        plt.axis(axes)\n",
    "    if iris:\n",
    "        plt.xlabel(\"Petal length\", fontsize=14)\n",
    "        plt.ylabel(\"Petal width\", fontsize=14)\n",
    "    else:\n",
    "        plt.xlabel(r\"$x_1$\", fontsize=18)\n",
    "        plt.ylabel(r\"$x_2$\", fontsize=18, rotation=0)\n",
    "    if legend:\n",
    "        plt.legend(loc=\"lower right\", fontsize=14)\n",
    "\n",
    "plt.figure(figsize=(8, 4))\n",
    "plot_decision_boundary(tree_clf, X, y)\n",
    "plt.plot([2.45, 2.45], [0, 3], \"k-\", linewidth=2)\n",
    "plt.plot([2.45, 7.5], [1.75, 1.75], \"k--\", linewidth=2)\n",
    "plt.plot([4.95, 4.95], [0, 1.75], \"k:\", linewidth=2)\n",
    "plt.plot([4.85, 4.85], [1.75, 3], \"k:\", linewidth=2)\n",
    "plt.text(1.40, 1.0, \"Depth=0\", fontsize=15)\n",
    "plt.text(3.2, 1.80, \"Depth=1\", fontsize=13)\n",
    "plt.text(4.05, 0.5, \"(Depth=2)\", fontsize=11)\n",
    "plt.title('Figure 6-2. Decision Tree decision boundaries')\n",
    "\n",
    "save_fig(\"decision_tree_decision_boundaries_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scikit-Learn使用CART算法，该算法仅生成二叉树：非叶节点总是有两个子节点（即，问题只有是/否答案）。 但是，其他算法（如ID3）可以生成具有两个以上子节点的节点的决策树。\n",
    "\n",
    "图6-2显示了决策树的决策边界。\n",
    "\n",
    "* **粗垂直线**表示根节点的决策边界（深度0）：花瓣长度= 2.45厘米。由于左侧区域是纯净的（仅Iris-Setosa），因此无法进一步拆分。 \n",
    "\n",
    "* 然而，右侧区域是不纯的，因此深度为1的右侧节点将其分割成花瓣宽度= 1.75厘米（由**虚线**表示）。由于max_depth设置为2，因此决策树会在那里停止。 \n",
    "\n",
    "* 但是，如果将max_depth设置为3，那么两个深度为2的节点将各自添加另一个决策边界（由**点虚线**表示）。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**模型解读：白盒与黑盒**\n",
    "\n",
    "正如您所见，**决策树非常直观**，而且他们的决策很容易解释。 这种模型通常被称为**白盒模型**。 相反，正如我们将要看到的，**随机森林或神经网络**通常被认为是**黑盒模型**。 他们做出了很好的预测，你可以轻松地检查他们进行的计算以做出这些预测; 尽管如此，通常很难用简单的术语解释为什么做出预测。 例如，如果一个神经网络说一个特定的人出现在一张图片上，那么很难知道这个预测究竟有什么贡献：模型是否认出了那个人的眼睛？ 她的嘴？ 她的鼻子？ 她的鞋子？ 甚至是她坐在沙发上？ 相反，决策树提供了简单的分类规则，如果需要，甚至可以手动应用（例如，用于花卉分类）。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.3 Estimating Class Probabilities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**估计类概率**\n",
    "决策树也可以估计一个实例属于一个特定的类 k 的概率：首先它遍历树以找到该实例的叶节点，然后它返回该节点中类 k 的训练实例的**比例**。\n",
    "例如，假设你发现了一朵花瓣长5厘米，宽1.5厘米的花。 相应的叶节点是深度为2的左节点，因此决策树应输出以下概率：\n",
    "* Iris-Setosa 为 0％（0/54），\n",
    "* Iris-Versicolor 为 90.7％（49/54），\n",
    "* Iris-Virginica 为 9.3％（5/54）。\n",
    "\n",
    "当然，如果你要求它预测类别，它应该输出Iris-Versicolor（类别 1 ），因为它的概率最高。 我们来检查一下："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.        , 0.90740741, 0.09259259]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tree_clf.predict_proba([[5,1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tree_clf.predict([[5,1.5]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "请注意，估计的概率在图6-2的右下方矩形中的任何其他位置都是相同的 - 例如，如果花瓣长6厘米，宽1.5厘米（尽管在这种情况下很可能显然是Iris-Virginica）。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.4 The CART Training Algorithm"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scikit-Learn使用**分类和回归树（Classification And Regression Tree-CART）**算法训练决策树（也称为“生长”树）。这个想法非常简单：\n",
    "该算法首先使用**单个特征 k 和阈值 $t_k$** （例如，“花瓣长度≤2.45cm”）将训练集**分成两个子集**。它如何选择 k 和 $t_k$呢？它为 $(k，t_k)$ 搜索产生最纯子集（按其大小加权）。算法试图最小化的成本函数由公式6-2给出:\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* 一旦它成功地将训练集分成两部分，它就会**使用相同的逻辑分割子集，然后递归地分割子子集等**。\n",
    "* 一旦达到**最大深度**（由max_depth超参数定义），或者如果找不到会减少杂质的分割，它就会停止递归。\n",
    "* 其他一些超参数（稍后描述）控制其他停止条件（min_samples_split，min_sam ples_leaf，min_weight_fraction_leaf和max_leaf_nodes）。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如你所见，CART算法是一种贪婪的算法：它贪婪地在顶层搜索最佳分割，然后在每个级别重复该过程。 它不检查分裂是否会导致几个级别的最低可能杂质。 贪心算法通常会产生一个**相当好的解决方案**，**但它不能保证是最佳解决方案**。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "不幸的是，找到最佳树是一个NP-Complete问题：它需要$O(exp(m))$时间，即使对于相当小的训练集，问题也难以处理。这就是为什么我们必须满足于“合理的”解决方案。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.5 Computational Complexity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "进行预测需要从根到叶子遍历决策树。决策树通常近似平衡，因此遍历决策树需要经过大致$O(log_2(m))$节点。由于每个节点仅需要检查一个特征的值，因此总体预测复杂度仅为$O(log_2(m))$，与特征的数量无关。 因此，即使在处理大型训练集时，预测也非常快。\n",
    "\n",
    "但是，训练算法会比较所有特征（如果设置了max_features，则会少一点）在每个节点的所有样本上。 这导致训练复杂度为$O(n×m log(m))。\n",
    "* 对于小型训练集（少于几千个实例），Scikit-Learn可以通过**预先分配数据**来加速训练（设置presort = True），\n",
    "* 但是对于较大的训练集来说，这会大大减慢训练速度。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.6 Gini Impurity or Entropy?"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**基尼杂质或熵?**\n",
    "\n",
    "默认情况下，使用Gini杂质测量，但您可以通过将标准超参数设置为“熵”选择entropy impurity来测量。熵的概念起源于热力学作为分子紊乱的度量：\n",
    "\n",
    "当分子仍处于有序状态时，熵接近于零。 它后来传播到各种各样的领域，包括香农的信息理论，它测量消息的平均信息内容：当所有消息相同时，熵为零。 在机器学习中，它经常被用作杂质测量：当一个集合的熵只包含一个类的实例时，它的集合为零。 公式6-3显示了第i个节点的熵的定义。 例如，图6-1中的深度2的左节点具有等于$-\\frac{49}{54}log(\\frac{49}{54})-\\frac{5}{54}log(\\frac{5}{54})≈0.31$的熵。\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "你应该使用基尼杂质还是熵？ 事实是，大部分时间它们并没有产生很大的不同：它们导致类似的树。基尼杂质的计算速度稍快，因此它是一个很好的默认值。 然而，当它们不同时，基尼杂质倾向于在树的自己的分支中隔离最频繁的类，而熵倾向于产生稍微更平衡的树。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Sensitivity to training set details**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.8, 1.8]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[(X[:, 1]==X[:, 1][y==1].max()) & (y==1)] # widest Iris-Versicolor flower"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DecisionTreeClassifier(class_weight=None, criterion='gini', max_depth=2,\n",
       "            max_features=None, max_leaf_nodes=None,\n",
       "            min_impurity_decrease=0.0, min_impurity_split=None,\n",
       "            min_samples_leaf=1, min_samples_split=2,\n",
       "            min_weight_fraction_leaf=0.0, presort=False, random_state=40,\n",
       "            splitter='best')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "not_widest_versicolor = (X[:, 1]!=1.8) | (y==2)\n",
    "X_tweaked = X[not_widest_versicolor]\n",
    "y_tweaked = y[not_widest_versicolor]\n",
    "\n",
    "tree_clf_tweaked = DecisionTreeClassifier(max_depth=2, random_state=40)\n",
    "tree_clf_tweaked.fit(X_tweaked, y_tweaked)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure decision_tree_instability_plot\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjgAAAEYCAYAAABRMYxdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAIABJREFUeJzt3XecVPX1//HXcVGqIAKCilRBBEWMYAU1sfDD2BINkaiRmASjXyUxMVFsQTFiEmOCxl4Cxo4Ba0STWBBFEbtYQJGidKTsUhZYzu+Pe3eZHWZmZ2en7Nx9Px+PebBzy+eee3fYPfu5n3M/5u6IiIiIRMkOhQ5AREREJNuU4IiIiEjkKMERERGRyFGCIyIiIpGjBEdEREQiRwmOiIiIRI4SHIkMM+tkZmVmVlLoWBqC8Fp3S7F+lpkdnUY7Z5rZC1kNroBq8zmMymfWzNzM9s5R21WfMzMbb2bX5eI4Ej1KcKTomNk8M9sQ/uCrfO3h7gvcvYW7VxQ6RgAza2Zmt5nZCjNbY2ZTa9h+qJl9YmalZvaxmZ1ai2MNNLPXw+N8Y2avmdmAup9FcuG1nhsef7tfPO7ex91fTqOdB939+Mr3dfllaWZHm9lXmewb7j/czKZluj9AbT6H9e0zC1X/v47NUdu1/v7Efs5EaqNRoQMQydBJ7v7ffB3MzBq5+5Za7nYXwf+xfYFvgH4p2t8TeAA4BZgCnABMNLMu7r6shthaAs8A5wOPATsBg4DyWsYraTCzkvqUkIhIEu6ul15F9QLmAccmWN4FcKBR+L4rMBUoBf4L3Ao8EK47GvgqWbvAaOBxgqRjLfAzgh7Py4AvgJUEycSuSWLsFe7XMs1zOgRYFrdsOXBYGvv2B1bXsM25wCfAKuB5oHPMOgd+AcwBVofXycJ1ewOvAGuAFcCjcfvtDYwANgObgDLg6djrCewBbIi9VsCBYXs7AsOBaeHyqWG768K2fgh8RJDQVu67Y7jvgXHn2Dw8ztZw37Lw2I2BvwGLwtffgMYJrtG+wEagItx3dbh8PHA78O8wrmOB7wLvht/jhcDoFJ/Dl4ExwGsEn8UXgLa13TZc/2NgPsHn7yqS/F8Itz0B+Dhs52vgkph1JwLvhd/v14G+4fJ/htdvQ3gNfpek7d8Ci8PreW7lZyFc1xi4EVgALAXuAJqm+P4cDEwPY1kM/B3YKf5zFvO9uC78ui1BYr+a4A+IV4EdCv3zSa/689ItKomyh4AZQBuChOXsWu5/CkGSswvwIHARcCpwFMEP5lUEyUAiBxP8IromvEX1oZmdluJYM4FPzOxkMysJb0+VAx+kEedsoMLMJpjZEDNrHbvSzE4BLge+D7Qj+EXwcFwbJwIDgL7AUGBwuHwMwS/Z1kBH4Jb4g7v7XQTX508e3E44KW79IoJfYLHn/yPgcXffHLftkeGXB4RtPQrcD5wVs9kJwGJ3fzdu33XAEGBRuG+L8NhXAIcS9KAdQPC9uTLBeXxCkOhND/fdJS7ePwA7A9MIEp0fE3w2vgucX8MtxR8BPwF2I+hhu6S225pZb+A24Exgd6AVsGeKdu4FznP3nYH9gBfDdg4E7gPOI/i/cSfwlJk1dvezCRKTk8Jr8Kf4Rs3s/4UxHQf0IEj4Yt0A9CS43nuHMV6d4vtTAVxMkLAcBhwDXJDivCr9BviK4DPdnuAzrrmHpIoSHClWT5jZ6vD1RPxKM+tE8Av7anff5O7TgKdqeYzp7v6Eu2919w0Ev/yucPev3L2cIGk63cwS3ertSPBLZQ1BMnQhMMHM9k10IA9uedxPkJSVh/+eF/5SSMnd1wIDCX643w0sN7OnzKx9uMkvgLHu/okHt9muB/qZWeeYZm5w99XuvgB4iW230zYDnYE93H1jeB0z8RAwDMDMDDgjXJaOB4ATwltxECSq/6zFsc8ErnX3Ze6+HLiG2ie7T7r7a+FnYaO7v+zuH4bvPyBIGI9Ksf8/3H12+Dl6jBS3K1NsezpB79g0d98EXE3qX+ibgd5m1tLdV7n7O+HyEcCd7v6mu1e4+wSCz9yhNV2E0NAwxo/Cz+foyhXh93YEcLG7f+PupQSftzOSNebub7v7G+6+xd3nESRcqa5l7PntTtAbudndX3V3JThSRQmOFKtT3X2X8JXoL+c9gG/cfX3MsoW1PEb89p2ByZWJFcEtnwqCvx7jbSD4AXxdmGC9QpA4HB9TOVNmZmUA4aDOPxHcOtuJ4Af8PWaW6hdhlTB5Ge7ulYnVHgS3YirjHhcT9zeAUf2v/yUxX68HWoRf/y7cdkZYFXVuOvEk8C/gMDPbHTiS4DbFq+nsGP6V/xpwmpntQtAL8GAtjr0HQW9apfnhstqo9lkws0PM7CUzW25mawiSyLYp9k92fWuz7R6xcYSf7ZUp2jmNoLdrvpm9YmaHhcs7A7+J+QNhNbAX6V+TanFQ/dq2A5oBb8e0PSVcnpCZ9TSzZ8xsiZmtJUiIUl3LSn8GPgdeMLO5ZnZZmvFLA6EER6JqMbCrmTWLWbZXzNfrCH4QA8HAUbb/IRz/1+BCYEhMYrWLuzdx968THD/RraVgQMG2ypkW7l75y6sfMNXdZ4a9Am8Bb7J993+N3P1TgrEK+8XEfV5c3E3d/fU02lri7j939z0IbmnclqTCKeVfzu6+iuBW1w8JbsE8Usu/ticQ3Kb6AUHPWqJrniyORQS/1Ct1Cpelu3+i5Q8R9Aju5e6tCMaZWJJ9s2UxQc8gAGbWlOAWU0Lu/pa7n0Jwq+sJgt4gCD4Pf4j7PDRz98rbljV9XxZT/f9Sp5ivVxAk931i2m4V8zlP1PbtwKdAD3dvSXCrqcZr6e6l7v4bd+8GnAz82syOqWk/aTiU4Egkuft8gnEto81sp/Cv19ixIbOBJmb2XTPbkWBMRuMamr0D+EPlrR0zaxeOb0lkKsFYhlFm1sjMjgC+TTDAN5G3gEGVPTbhOIlBpDEGx8x6mdlvzKxj+H4vgttBb8TEPcrM+oTrW5nZD2pqN9z2B5XtEow5coLel3hLgaTPxAk9RDBu5XRS355K1NYTwLeAXxLcyku1bxszaxWz7GHgyvD71Zbg1s4DKfbvaGY7pTgGBGNxvnH3jWZ2MEHSlmuPAyeZ2eFhfKNJkgiEn/kzzaxVOM5pLdu+b3cDvwh7oczMmof/D3YO19f0vXwMGG5mvcM/IH5fucLdt4bt/9XMdgtj2dPMKsd0Jfr+7BzGV2ZmvQiqAWtkZiea2d7hbbE1BL2piT6b0kApwZEoO5Ng0OJK4DrgUcLSaXdfQzCQ8R6CCpN1BAMWUxlH8Ff7C2ZWSpBAHJJow/CXyikEtwjWEPzQ/3HYu5Jo+1cIK7fCtv8FXO/uL0DVw/BmJYmrNIzjTTNbF8b1EcEgTNx9MvBH4JHwFsBHBLd50jEgbLcsPPdfeuJnktxLMN4j4Zio0FMEg1KXuPv7KY45mmC80mozGxqewwaCa9IVmJRsx/D6PgzMDfffg+B7P5MgWfwQeCdclsiLwCxgiZmtSBHjBcC14ffqarb1juSMu88iGOj+CEEvShmwjOSPAzgbmBd+z39B8P8Bd58J/JygWmkVwW2e4TH7jSVICFeb2XaDod39OYLbny+G+74Yt8ml4fI3wmP/F9gn3DfR9+cSggSxlOD/yaPpXRF6hG2XEQxiv83dX0pzX2kAKktBRSLPzB4FPnX339e4sdQ7ZnY10NPdz6px4wbAzFoQlEj3cPcvCx2PSH2jHhyJLDMbYGbdzWwHC0pbTyG41SFFxsx2BX5K8PDEBsvMTrLgCdnNCZ418yHBs3BEJE5eExwze8DMFpvZWjObbWY/S7HtxZWj6s3sPjOraXyESLwOBA9OKwNuBs73uGenSP1nZj8nGBj7nLunnO6iATiFbQ8s7AGcodJokcTyeosqHOT4ubuXh4PJXga+6+5vx203mGAg4XcI/iNPBt5wd5UBioiISI3y2oPj7rM8eEAaBNUYDnRPsOk5wL3h9qsInqY6PD9RioiISLHL+2SbZnYbQbLSlGAul38n2KwP8GTM+/eB9mbWxt2rPdjKzEYQPDmTZs2bHdS9V6J8SURERKLgw7c/XOHuSR8eWSnvCY67X2BmFxGU7x5N4hLHFgSltZUqv96ZuCd3ejAPzl0Affv39WdnPJvtkEVERKSe6FTSaX7NWxWoiiqc/2QawVM5Ez3UqQxoGfO+8uvSXMcmIiIixa/QZeKNSDwGZxbBrL+VDgCWxt+eEhEREUkkbwmOme1mZmeYWQszKwkrpYYB/0uw+f3AT8NHge9C8Bj98fmKVURERIpbPntwnOB21FcEjwe/EfiVuz9l22ZX7gTg7lMIZlZ+iWA+n/nEzHciIiIikkreBhm7+3LgqCTrFhAMLI5ddhNwUx5CExERkYgp9BgcERERkaxTgiMiIiKRowRHREREIkcJjoiIiESOEhwRERGJHCU4IiIiEjlKcERERCRylOCIiIhI5CjBERERkchRgiMiIiKRowRHREREIkcJjoiIiESOEhwRERGJHCU4IiIiEjlKcERERCRylOCIiIhI5CjBERERkchRgiMiIiKRowRHREREIkcJjoiIiESOEhwRERGJHCU4IiIiEjlKcERERCRylOCIiIhI5CjBERERkchRgiMiIiKRk7cEx8wam9m9ZjbfzErN7D0zG5Jk2+FmVmFmZTGvo/MVq4iIFJelpUv5wYQfsKxsWc7bzMWxJPvy2YPTCFgIHAW0Aq4EHjOzLkm2n+7uLWJeL+clShERKTrjXh3HjIUzGDd1XM7bzMWxJPvyluC4+zp3H+3u89x9q7s/A3wJHJSvGEREJHqWli5l4vsTcXcmvj8xKz0rydrMxbEkNwo2BsfM2gM9gVlJNjnQzFaY2Wwzu8rMGiVpZ4SZzTSzmd8s/yZn8YqISP007tVxuDsAW31rVnpWkrWZi2NJbhQkwTGzHYEHgQnu/mmCTaYC+wG7AacBw4DfJmrL3e9y9/7u3n/XdrvmKmQREamHKntUNlVsAmBTxaY696wka/PjJR9n/ViSO3lPcMxsB+CfwCbgwkTbuPtcd/8yvJX1IXAtcHoewxQRkSIQ26NSqa49K8naHDl5ZNaPJbmT8LZPrpiZAfcC7YET3H1zmrs6YDkLTEREitI7X71T1aNSaVPFJt7+6u2stzl/9fysH0tyJ68JDnA7sC9wrLtvSLZRWD7+jrsvNbNewFXAxDzFKCIicZaWLuXCSRdy62m3sluL3QoWx6wlsxh6/1AmnjOR3u17M2XElKwfIxdtSv7l8zk4nYHzgH7Akpjn25xpZp3CrzuFmx8DfGBm64B/A5OA6/MVq4iIVFdfSqNHTh5JaXkpIyeNLGgcUv/ls0x8vrubuzeJe77Ng+6+IPx6QbjtJe7e3t2bu3s3d7+6FrezREQki+pLafSsJbOYs2IOALNXzObjpR8XJA4pDpqqQUREUqovpdEjJ1fvtVEvjqSiBEdERJLKRRl2JmJ7byqpF0dSUYIjIiJJ5aIMOxPxvTdVy9WLI0kowRERkaRyUYadiQWrFyRcPn/1/LzGIcVDCY6IiCQ1ZcQUFly1gLd+9RaHdDqEmRfPZMFVC6qVUmcy63ZtZ+SeM2oOC65asN1rzqg5GbWXaRx1OVYxiNK5KcEREZEapSoTz2TW7WyXnWfaXib71ZeS+VyI0rkpwRERkZRSlYlnMut2tsvOM20vk/3qS8l8LkTt3JTgiIhISqnKxDOZdTvbZeeZtpfJfvWlZD4XonZuSnBERCSpVGXiydbNWjKr1vtk2luQaXuZ7FdfSuZzIYrnpgRHRESSSlUmnmzdLyf/stb7ZNpbkGl7mexXX0rmcyGK55bvyTZFRKSI1FQmnsms29ksO8+0jD2T/epLyXwuRPHcLD5jK2Z9+/f1Z2c8W+gwREQkRzKZ1by+zISeT1E+504lnd529/41badbVCIiUjRU1p2ehnjO8ZTgiIhIUVBZd3oa4jknogRHRESKgsq609MQzzkRJTgiIlLvqaw7PQ3xnJNRgiMiIvWeyrrT0xDPORklOCIiUu+prDs9DfGck1GZuIiI5F2qMuZM1mVaFl3M5dTFHHtdqExcRETqrUxnGs9k5vJM46jvijn2fFCCIyIieZXpTOOZzFyeaRz1XTHHni9KcEREJK8ynWk8k5nLM42jvivm2PNFCY6IiORNJrOTZzpzeaZx1HfFHHs+KcEREZG8yWR28kxnLs80jvqumGPPJ80mLiIieZPJ7OR1mbk80zjqs2KOPZ/yViZuZo2B24BjgV2BL4BR7v5cku0vBi4FmgGPA+e7e3mqY6hMXEQktWyXZ9e0TtKT7WsY5e9JfSwTbwQsBI4CWgFXAo+ZWZf4Dc1sMHAZcAzQGegGXJOvQEVEoirb5dk1rZP0ZPsa6ntSiwTHzJqZ2eFmdqqZfT/2lc7+7r7O3Ue7+zx33+ruzwBfAgcl2Pwc4F53n+Xuq4AxwPB0YxURke1luzy7pnWSnmxfQ31PAmklOGZ2LDAfmAZMIrhlVPmamMmBzaw90BOYlWB1H+D9mPfvA+3NrE2CdkaY2Uwzm/nN8m8yCUVEpEHIdnl2TeskPdm+hvqeBNLtwRkHPAt0dPcd4l4ltT2ome0IPAhMcPdPE2zSAlgT877y653jN3T3u9y9v7v337XdrrUNRUSkQch2eXZN6yQ92b6G+p5sk26C0wUY4+6L6npAM9sB+CewCbgwyWZlQMuY95Vfl9b1+CIiDVG2y7NrWifpyfY11Pdkm3TLxF8D9iGofMqYmRlwL9AeOMHdNyfZdBZwAPBY+P4AYKm7r6zL8UVEGqpsl2ens05qlu2Sb5WQb5O0TNzMvhXztgtwHXAT8CFQLTFx93fSOpjZHUA/4Fh3L0ux3f8DxgPfARYRjPuZ4e6XpWpfZeIiIplLVVo8a8ksht4/lInnTKR3+951bq+YRfW8ikU2ysRnAm+F/z4O9ALuAqaHy2bGbFMjM+sMnEeQ4Cwxs7LwdaaZdQq/7gTg7lOAPwEvAQsIBjj/Pp3jSP0w/eXpdN2pa6HDEJFaSFVaPHLySErLSxk5aWRW2itmUT2vqEmV4HQleP5M1xpe3dI5kLvPd3dz9ybu3iLm9aC7Lwi/XhCz/U3u3t7dW7r7T2p6yJ8kNvQ7Q9m76d7s22pf+rTuwxF7H8Evf/xLPnj7g6wdY+L4iQzqOShr7SXy56v+zJCDhtC9SXeGHT8sp8cSaYhSlRbPWjKLOSvmADB7xWw+XvpxndorZlE9ryhKmuCECcl8d59P8LC9r2OXhcu/DtdJPTbyypF8suYTZq2axaP/e5SOnTty6uGnMmXylEKHlrbO3Trz69G/5kc//1GhQxGJpFSlxSMnV++1SacXJ6qlylE9ryhKt4rqJYLpFeK1CtdJkejYuSO/HfNbTjv7NK7+5dW4OxvWb+C6317HEd2PYP+2+3P2kLOZ9/m8qn2Gfmcooy8ezfCThtOrZS+O2f8YXnou+La/Pf1tLr/gchbMXUCvlr3o1bIX01+eXrXvU48+xcAeA+nTug/n//B8ykqTDr1KaehPhnLcScfRum3rOp2/iGwvVWlxbO9NpZp6caJaqhzV84qqdBMcAxKNRm4DrMteOJIvJ/3wJJZ8vYQvPvuCS0dcyueffs4Trz/B24vept8h/fjJyT9h8+ZtY8kfve9Rzh15Lh998xEXXnYhI04bwcJ5CznosIO4/rbr6dStE5+u/ZRP137KYUcfBkBFRQWv/udVnn/3eV7+9GVmvTeLf9zyj6o2h580nP123S/p64mHnsj7dRFpiFKVFsf33lRK1YsT1VLlqJ5XVKUsEzezp8IvHXjAzGLHwZQA+wGv5yg2yaHdO+4OwIqlK3ji4SeY/uV02rVvB8DFV1/MfePu49033+XggQcDcPwpx3PkcUcC8L0zv8c/7/wnTz78JBeOSvYoo8BlYy+jeYvmNG/RnMGnDOaDmdvG/ox/enwOzkxEaitVafGC1QsS7jN/9fyM2itmUT2vqKrpOTiVz50xYBWwIWbdJoKpG+7OQVySY4u/WgyA7WAADO43uNr6zZs3s3jh4qr3e3XZq9r6vTrvVdVGMiUlJbRpt212jabNm1JWltktKhGpnWRl3YmWTxlR83i82pRGp9NeJrHXNo667JNov7qel8rL8yvlLaqweuknBDN5/7Tyffg6z93HuvuK/IQq2fTMY8/QYc8OdOsZFMG98tkrfPTNR1Wv2WWzOWXYKVXbL5y3sNr+C+cvrOoFqkySauvHJ/y4atxOotfkBydneHYikqysO5Nyb8hvaXSqGDOJI9PYNcN3cUtrDI67X+PuGmsTAYsWLuIvo//CxAkTGf3X0bRr345Th53KFf93BUu+XgLAmtVrmDJ5CuvKtn3LX3jyBab9bxoVFRU8+fCTfDjzQ04+42QAduuwGyuXraR0be1m0rj/3/dXjdtJ9Premd+r2nbz5s1s3LiRii0V+FZn48aNlJfryQEiiSQr686k3BvyWxqdKsZM4sg0ds3wXfySJjhm9qWZzU3nlc+ApfZuvu5m9m21L7136c0Pjv4B8z+fz+RpkznhtBMA+ONdf6T7Pt0Z+p2h7NtqX44/4HieffxZgpk1Aj8894fc89d76NO6D+OuG8cdE++gU9dOABz27cMYdOwgjuh+BPvtuh9vvPJG1s/h0hGX0rN5T265/hZef+l1ejbvybf3/XbWjyMSBcnKujMp94b8lkanijGTODKNXTN8F79UUzX8JuZtC+DXwAyCJxkDHAYcDPzF3a/NZZDp0lQNuTH0O0MZeMxARl5Ruy5tEcm/WUtmMeTuIdstv/X7t/J/k/5vu+VTRkxJOfXC0tKlDPz7QMq3bOsxbdKoCdMumpb1cSTJYp8yYgptmrWpdRyZxp7tc87nNWwI6jxVg7v/pfJF8MTiP7r7ce5+dfg6DrgB6Jm9sEVEpC6SlXVf/MTFibevoRcnn6XRqUrSM4kj09g1w3dEuHuNL2AtsHeC5XsDa9NpIx8vgnL2aq9hPxvmCyoW+IKKBdut0/r01h961KF+ybWX1Nv4tF7rtT7xer6FMzp8JVnf+LrGKdvvfXvvpPvnK/7G1zVOur737b2T7r/LwF1Snn9dr1+659f79t5J46vPn596vH5mOjlBug/6WwccnWD50cD6NNuQIvXYi4/p9pRIDi0tXZqTdod9axgLrlrAgqsSP8tm2LeGMWfUHA7aY4+E6yc/2JwpI6Yk3T/XKuOfM2pO0vWpSreH9BqS8vzTPX5dzz9ZjEN6bX87TrIn6RicahuZ/Q4YA/wDqBxBeihwDjDa3f+YswhroW/f/v7UUzMLHYaISK1c9cYFPPjZnZy5zy8Yc+iteT9+167J1335Zf7iEElH165WtzE4sdz9T8DZwP7ATeFrf+Cc+pLciIgUo2XrFzPx83/gbOXxz//B8g1LCh2SSCSke4sKd3/M3Y9w913D1xHu/lgugxMRibpbPhjDVt8KQIVXcPP7YwockUg0pJ3giIhIdlX23mzeGsxvtHnrJvXiiGRJqgf9rTWztuHXpeH7hK/8hSsiEh2xvTeV1Isjkh2pJtu8CCiN+brm0cgiIpK2d5ZNr+q9qbR56ybeWfZ6XuNo2xZWJJhVsG3bvIYhklVJExx3nxDz9fi8RCMi0oA8e/K7hQ4BgLfeKnQEItmXqgenipldDrwEvOXuW3IbkohIwzBgQPKek1RJR6b7ZSKfx8qVZesXc9HUM/j7UY/SrmmHQocjeZLuIOMhBAnOKjN7wcwuN7PDzSytBElERLaXKHFItbyu+2Uin8fKlVs+GMNbS6dpbFMDk+5zcAYBrYHvAW8SJDz/I0h4ns9deCIiIpnTc4Yarto8B2eDu/8X+DtwG/AvoDEwKEexiYiI1ImeM9RwpZXgmNlQM7vNzD4B5gI/B+YAxxH07IiIiNQres5Qw5ZuD84jwGnAfUA7d/+Ou1/j7q+4e3nuwhMREcmMnjPUsKWb4IwAXiB4Hs4iM3vazH5jZt8yM0v3YGZ2oZnNNLNyMxufYrvhZlZhZmUxr6PTPY6ISDFI9pyZmp4/k+l+mcjnsbKtvjxnSAojrSood78HuAfAzLoDRxPcnroeKAPapHm8RcB1wGCgaQ3bTnf3gWm2KyKSc9kumU5VoZTqWJno1g08weNazWDu3ODrROXUledVjKXW9eU5Q1IYaQ8yNrMdzOwQ4HRgKHAiYMDsdNtw90nu/gSwsraBiogUWn0pz84kjkTJTfzyVOXUKrWWYpPuIOPngFXAq8CpwDsEY3Jau/thOYrtQDNbYWazzewqPXNHRCR3UpVTq9RailG6PTjvEfTatHb3w9x9lLs/7+7rchTXVGA/YDeCRGoY8NtEG5rZiHBcz8yVK5fnKBwRkWhLVU6tUmspRuk+6C/XCU388ea6+5fuvtXdPwSuJbg1lmjbu9y9v7v3b9OmXT7CExGJlFTl1Cq1lmKV9hicAnOC8T4iIpJlqcqpVWotxSqvCY6ZNTKzJkAJUGJmTRKNrTGzIWbWPvy6F3AV8GQ+YxURiVdfyrMziSPZAz3MUpdTq9RailW+B+5eCfw+5v1ZwDVmdh/wMdDb3RcAxwDjzawFsBR4gKAkXUQkbdku68509ux0SrTjDRiQvL2VSepQV67M9JyLp5y6GMvVpTDy2oPj7qPd3eJeo919gbu3CJMb3P0Sd2/v7s3dvZu7X+3um/MZq4gUv/oyE3Y6JdrxUsWeqr36cs65onJ1SVexjMEREZEGTuXqUhtJExwzKzWztem88hmwiIg0TCpXl9pINQbnwrxFISIikkKycvWRB1ylsTiSUNIEx90n5DMQERGRZFKVq4859NYCRSX1mcbgiEhk1ZeZsFOVaCeTKvZU7dWXc842latLbaVVJm5mOwFXEEyZ0AnYMXa9u5dkPzQRaUiyXdINyffr2jV4JWKWvKQbMlvXpk3yKqZEcdSUjCQrLY8yzQwutZVuD84Y4BzgL8BWgnmhbiWYFfyC3IQmIg1JfSlvTlWCnem6ZOeQbJ9MZwwXkW3STXCGAr9w9zuBCuBJdx9J8NC+43IVnIiIiEgm0k1w2hM8aRigDNgl/HoKcHy2gxIRERGpi3QTnAXAHuEvcXxSAAAZIklEQVTXnwODw68PAzZkOygRERGRukg3wZlMMD8UwDiC+aO+BMYD9+QgLhEREZGMpVVF5e6jYr5+3MwWAkcAs939mVwFJyINR9u2yauo8imfVVTJjlV5zvXheogUq3TLxI8EXnf3LQDu/ibwppk1MrMj3X1qLoMUkejLtBQ8lWSl56kSi1RxJGuvTZua90ukpv1qG0ddSupFoibdW1QvAbsmWN4qXCciUu9kUp6dSXu52i9f7YlEUboJjgGJfiS0AdZlLxwRERGRukt5i8rMngq/dOABMyuPWV0C7AfoOdkiIiJSr9Q0Bmdl+K8Bq6heEr4JmAbcnYO4RERERDKWMsFx958AmNk84EZ31+0oERERqffSGoPj7te4+zoz629mPzSz5gBm1tzM0qrEEhHJt2Ql1clm466pBDvTmbqzPcN3VGcMF8mmdMvE2wNPAgcTjMfpAcwFbgI2Ar/MVYAikh1RLS1OdV7JZFqene1ZzTNVzN8vkXxJt4rqr8BSgqqp9THLJ6K5qESKQlRLi1OdV1TPWURqlu7tpWOAY9x9lVXv2/0C6JT1qERERETqIN0enKYEVVPx2hHcohIRERGpN9JNcKYCw2Peu5mVAJcC/8t2UCIiIiJ1ke4tqt8Br5jZAKAx8BegD8FUDUfkKDYRERGRjKRbJv4x0BeYDrwANCEYYHygu3+Ru/Ckrv72t9F07Wp07Wp067YDBxzQmlNOGcCf/3wFy5cvyckx586dzd/+Npq1a1dXW/744+Pp2tVYt64s68d0d2699XoOP3wvevVqytChR/Lxx+9l/TjFLKqlxanOK6rnLCI1S/sZNu6+GLi6LgczswsJbnXtDzzs7sNTbHsxwS2wZsDjwPnuXp5se0lu551bMWHCFADWrl3DrFnv8OCDt/PII3cxfvwU9t//oKwe78svZzNu3DWcfvpwWrbcJattJ3P77Tdwyy1jGDXqz3Tv3ot7772Js846luef/4h27TrkJYb6Ltulxd26JZ600gzmzs3uftkucR8wALp2TdweRLOcXqShSdmDY2bNzOxWM/vazJaZ2UNmVpe/fRYB1wH31XDcwcBlBNVbnYFuwDV1OG6D1qhRIw488FAOPPBQjjpqMBdcMIrnnvuAdu12Z+TIM6ioqCh0iHVSXr6RO+64gQsuGMU551zIwIHHcuutEzEzJkz4e6HDi6xkM3InW16X/fI5G7dKy0WioaZbVNcQ9Lg8CzwCHAfcnunB3H2Suz/BtjmukjkHuNfdZ7n7KmAM1Qc5Sx21bLkLo0b9iXnzPmfatP8AQaIwduzvOPzwvdhnn8YMGXIAL73072r7DRzYhT/84RJuvnkMAwZ0oE+fFvzqV2eydu0aAN5442V+9rOTABg0qCtduxoDB3ap1sbChV9y1lnH0bt3c445phdTpkyq07m8/fbrlJau5bvfHVq1rFmz5hxzzEm88spzdWpbRESKU00JzveBn7r7CHcfCXwXODWsoMqlPsD7Me/fB9qbWZv4Dc1shJnNNLOZK1cuz3FY0XLooUfTqFEj3n33DQAuuOB0/vWv8VxwweXcfffT9O07gJ///OTtxrI8/fTDvPbafxk79m6uuOImXnzxWS677GcA9OnzLS6//EYA7rhjEpMmTefOOydX2/9Xv/oRxx57MnfcMZkuXXowcuQZLF78VdX6rVu3smXLlpSv2F6nL774lJKSErp06VHtON2778sXX3yavQsmIiJFo6YxOHsBr1a+cfcZZrYF2ANYmMO4WgBrYt5Xfr0zcb0/7n4XcBdA3779a+gcl1iNGzehdeu2rFixlNde+x8vvvgsDz/8MoceehQARx55PF9+OZu///0P3HbbxKr9Nm7cwH33PUvz5i2AoLfk178+m88//4S9996Xbt32AaBPnwPp2LHLdsc999yLGTr0XAD23/8gBgxoz4svPsOZZ/4CgJtvvpZx41Lfkdxzz85MmzYPgDVrVtGsWQtKSqrn3a1atWbDhvVs2rSJnXbaqfYXSEREilZNCU4J2z/gb0sa+9VVGdAy5n3l16U5Pm6D4+HAh9de+y/t2nWgf/8j2LJlS9X6I444hscfH19tn4EDj6tKbgAGD/4e7s7777/F3nvvW+MxBw3aNrtH69ZtaNNmt2o9OMOGjeA73zkxZRs77dS4xuOIiEjDVVOiYsADZhZbvdQEuNvMquakcveTsxzXLOAA4LHw/QHAUnevaeyO1EJ5+UZWr15J27btWbLka5YvX0KPHjtut118z0ibNrtVe9+0aTOaN2/B8uWL0zpufGXVjjvuRHn5tgdit2vXYbtjxIudMqRVq9asX19GRUVFtVjXrFlF06bN1HuTI2bJq6GyvV/btrWfUDOVmtrL5rFEpDBqSnAmJFj2QKYHM7NG4TFLgBIzawJscfctcZveD4w3swcJKq+uBMZnelxJbPr0l9iyZQsHHngY06e/SIcOe3LnnU/UuN/Klcuqvd+wYT3r1pXRrt3uWYmrtreounfvRUVFBfPmfU737vtUbTN37qd0794rKzHJ9lKVgmd7P83GLSK1lTLBcfefZPl4VwK/j3l/FnCNmd0HfAz0dvcF7j7FzP4EvEQwD9a/4vaTOlq7djU33HApXbrszcCBx2Jm3HPPX2jevEWNScG0af9h3bqyqttUzz8/GTOjb9/+QNAjA1TrlamN2t6iOuigw9l555b8+98TueiiK4Eg6frf/57mjDNGZBSDiIgUt1yPpanG3UcDo5OsbhH7xt1vAm7KcUgNwpYtW6oqpcrKSvnoo7d54IHb2bhxPePHT6GkpIRBg47jyCMHc/bZx3HeeZfSs2cfSkvX8skn71FevpHf/W5sVXtNmjTl3HO/y4gRv2XZssWMHftbBg/+Hj169AaoGmT80EN3cuKJZ9C0aTN69do/7Xjbt9+D9u33SHv7xo2b8ItfXMYtt4yhVavWVQ/627p1K+ecc1Ha7YiISHTkNcGRwigtXcP3v38YZkaLFi3p0mVvTj31LIYPv6jqKb9mxu23T+K2267nH//4G4sWLaBVq13p3bvfdknCiSeeQYsWO3PppT9l/foyjj32ZK67btvjkTp27Mzll9/I+PE3M2HCLXTo0LHqdlKunH/+ZWzdupXbbx/LqlUr2X///vzzn/+hXbv2OT2uiIjUT+Y1PXa0iPTt29+fempmocOItIEDuzBkyOlcccWNhQ5FREQaoK5d7W1371/TdmlNtikiIiJSTJTgiIiISORoDI7USq7H0oiIiGSDenBEREQkciI1yNjMonMyIiIikogGGYuIiEjDFKkxOAcd1JcZM54vdBgiIiKSIyUl6U0LpB4cERERiRwlOCIiIhI5SnBEREQkcpTgiIiISOQowREREZHIUYIjIiIikaMER0RERCJHCY6IiIhEjhIcERERiZxIPclYisPSpZOYN28s5eVf07jxnnTpMor27b9f6LBERCRClOBIXi1dOok5cy5h69YNAJSXf8WcOZcAKMkREZGs0S0qyat588ZWJTeVtm7dwLx5YwsUkYiIRJESHMmr8vKva7VcREQkE0pwJK8aN96zVstFREQyoQRH8qpLl1HssEPTast22KEpXbqMKlBEIiISRRpkLHlVOZBYVVQiIpJLeU1wzGxX4F7geGAFMMrdH0qw3WjgCqA8ZnFfd5+bjzglt9q3/37ShEYl5CIikg357sG5FdgEtAf6Ac+a2fvuPivBto+6+1l5jU4KSiXkIiKSLXkbg2NmzYHTgKvcvczdpwFPAWfnKwap31RCLiIi2ZLPQcY9gS3uPjtm2ftAnyTbn2Rm35jZLDM7P1mjZjbCzGaa2czly1dmM17JM5WQi4hItuQzwWkBrI1btgbYOcG2jwH7Au2AnwNXm9mwRI26+13u3t/d+7dr1yab8UqeqYRcRESyJZ8JThnQMm5ZS6A0fkN3/9jdF7l7hbu/DowDTs9DjFJAKiEXEZFsyWeCMxtoZGY9YpYdACQaYBzPActJVFJvtG//fXr0uJHGjTsCRuPGHenR40YNMBYRkVrLWxWVu68zs0nAtWb2M4IqqlOAw+O3NbNTgKnAamAAMBK4PF+xSnWZlG6/995Q1q59tep9y5aD6NfvsYzby0WMIiISXfkuE78AuA9YBqwEznf3WWY2CHjO3VuE250RbtcY+Ar4o7tPyHOsQmal2/HJDcData/y3ntD2X33M5K2B2RUJq7ychERiWfuXugYsqZ//wN8xoznCx1GpLz55gDKy7/abnnjxh055JC3Eu4zderuSdtr3Lhj0vaAWh8r0xhFRKQ4lZTs/ra7969pO03VICllu3Q7k/ZqOpbKy0VEJJ4m25SUsl26naq9TI+l8nIREYmnBEdSyqR0u2XLQUmXp2ov0zJxlZeLiEg83aKSlDKZ/btfv8dSVlHV1F5tq6E0Q7mIiMTTIGMREREpGhpkLFkze/ZlLFnyAFABlNChw1n07HkDkPx5N5k+l0bPsxERkWxQgiMpBclN7COIKqrer18/N+HzbmbMOJpNmxboeTYiIlIwGmQsKQU9N4mXxyc3lTZu/KwqSam0desG5s0bm/JY8+aNzWg/ERGReEpwpAYVtVyenJ5nIyIi+aIER2pQUsvlyel5NiIiki9KcCSlDh3OSro82fNumjTZR8+zERGRglKCIyn17HkDHTqcw7YemxI6dDiHnj1voF+/x7ZLclq2HMTBB79Mjx43hvNLGY0bd6RHjxvTep5NJvuJiIjEUxVVBGVSap2qFHz16jfYNuamInwfWLt2erV2Kt9/9tlvgI1AUA312We/qYrh9dcPZMuWJVX7NGrUgcMPfzfj8wWVl4uISHV60F/ExJdaQ3CbJ1VPyPal4IEOHc5h9eo32Ljxs+3WNWmyDxs3fgFsqUV0TWjUaJdqyU2lRo060L37VbWOHTI7ZxERKU7pPuhPt6giJpNS61Sl4ImSGyBcXpvkBmBjwuQGYMuWJRmXiau8XERE4inBiZjMSq2zVwpeF5mWiau8XERE4inBiZjMSq2zVwpeF5mWiau8XERE4inBiZhMSq1TlYI3abJPwnXB8tqOUW9Co0YdEq5p1KhDxmXiKi8XEZF4qqKKmMpBtbWpKKqslkpWRTVjxtHVxuI0abIPBx/8MgBTp+5F9bE4jTjyyIVMndqVyiqqcC+OPPJLoOYqqtpWQ2VyziIiEm2qompAclFKnay8PFXZuYiISKbSraJSD04DkYuZupPNNL59afm2GciV5IiISD5oDE4DkYtS6mTl5clKy5NtLyIikm1KcBqI3JRS17aMPL9l5yIi0nApwWkgclNKXdsy8vyWnYuISMOlBKeByEUpdbLy8mSl5cm2FxERyTYlOA1ELmbqTjbT+MEHv5x0BnIREZF8yGuZuJntCtwLHA+sAEa5+0MJtjPgBuBn4aJ7gMu8hmBVJi4iIhJt9bVM/FZgE9Ae6Ac8a2bvu/usuO1GAKcCBwAO/Af4Ergjj7GKiIhIkcrbLSozaw6cBlzl7mXuPg14Cjg7webnAH9x96/c/WvgL8DwfMUqIiIixS2fPTg9gS3uPjtm2fvAUQm27ROui92uT6JGzWwEQY8PQHlJye4fZSHWqGhLcCtQdC3i6Xpso2tRna5Hdboe29SXa9E5nY3ymeC0ANbGLVsD7Jxk2zVx27UwM4sfh+PudwF3AZjZzHTuyzUUuh7b6FpUp+uxja5Fdboe1el6bFNs1yKfVVRlQMu4ZS2B0jS2bQmU1TTIWERERATym+DMBhqZWY+YZQcA8QOMCZcdkMZ2IiIiItvJW4Lj7uuAScC1ZtbczI4ATgH+mWDz+4Ffm9meZrYH8BtgfBqHuStb8UaErsc2uhbV6Xpso2tRna5Hdboe2xTVtSjEc3DuA44DVhI82+YhMxsEPOfuLcLtDPgj1Z+Dc6luUYmIiEg68prgiIiIiOSDpmoQERGRyFGCIyIiIpETiQTHzHY1s8lmts7M5pvZjwodU6GY2YVmNtPMys1sfKHjKSQza2xm94afiVIze8/MhhQ6rkIyswfMbLGZrTWz2Wb2s5r3ijYz62FmG83sgULHUkhm9nJ4HcrC12eFjqnQzOwMM/sk/N3yRThetEGJ+TxUvirM7JZCx5WOfM9FlSvpznHVECwCrgMGA00LHEuhNQIWEjwtewFwAvCYme3v7vMKGVgBjQV+6u7lZtYLeNnM3nX3twsdWAHdCrxV6CDqiQvd/Z5CB1EfmNlxBMUuPwRmALsXNqLCqCz+ATCzFsASYGLhIkpf0ffg1HKOq8hz90nu/gRBlVqD5u7r3H20u89z963u/gzBpK0HFTq2QnH3We5eXvk2fHUvYEgFZWZnAKuB/xU6Fql3rgGudfc3wp8fX4dzIzZkpwHLgFcLHUg6ij7BIfkcVwnnrpKGy8zaE3xeGmLPXhUzu83M1gOfAouBfxc4pIIws5bAtcCvCx1LPTLWzFaY2WtmdnShgykUMysB+gPtzOxzM/vKzP5uZg29V/wc4P5ieWRLFBKc2sxxJQ2Ume0IPAhMcPdPCx1PIbn7BQT/PwYRPHyzPPUekTUGuNfdvyp0IPXEpUA3YE+CB7o9bWYNtXevPbAjcDrB/5N+wIHAlYUMqpDMrDPB7f4JhY4lXVFIcGozx5U0QGa2A8ETszcBFxY4nHrB3SvC27kdgfMLHU++mVk/4Fjgr4WOpb5w9zfdvdTdy919AvAawbi1hmhD+O8t7r7Y3VcAN9FwrwcEwz6mufuXhQ4kXVEYZFw1x5W7zwmXae4qAaqein0vwV9kJ7j75gKHVN80omGOwTka6AIsCD4itABKzKy3u3+rgHHVJw5YoYMoBHdfZWZfEVyDqsWFiqee+DFwQ6GDqI2i78Gp5RxXkWdmjcysCVBC8AO7iZlFIZHN1O3AvsBJ7r6hpo2jzMx2C8teW5hZiZkNBobRMAfY3kWQ2PULX3cAzxJUHzY4ZraLmQ2u/HlhZmcCRwJTCh1bAf0DuCj8f9MauBh4psAxFYSZHU5w67IoqqcqReUX3wUEc1wtI6geOr+BlohDcI/49zHvzyKoBhhdkGgKKLxnfB7BGJMl4V/qAOe5+4MFC6xwnOB21B0Ef9zMB37l7k8VNKoCcPf1wPrK92ZWBmx09+WFi6qgdiR4vEQvoIJgAPqpccUbDc0YoC3BXYKNwGPAHwoaUeGcA0xy96Ia+qG5qERERCRyiv4WlYiIiEg8JTgiIiISOUpwREREJHKU4IiIiEjkKMERERGRyFGCIyIiIpGjBEdE6h0zGx4+mybVNvPM7JJ8xZSKmXUxMzez/oWORUQCSnBEJCEzGx/+0nYz22xmc83sRjNrXss2IvX01yiek0gUReVJxiKSG/8lmGRvR4JZle8BmtMAJ+gUkeKiHhwRSaXc3Ze4+0J3fwh4EDi1cqWZ9TazZ82s1MyWmdnDZtYhXDea4BHv343pCTo6XHeDmX1mZhvCW01/CudQy5iZtTKzu8I4Ss3sldhbRpW3vczsGDP7yMzWmdlLZtY1rp1RZrY03PZ+M/u9mc2r6ZxCnc3sP2a23sw+NrPj6nJOIpI5JTgiUhsbCHpzMLPdganAR8DBwLEEs3I/aWY7ADcSzN/zX2D38PV62M464FyCiVAvAM4Arsg0qHDW+GcJJgQ8ETgwjO3FMM5KjYFR4bEPA3YhmJursp0zCOZyuwL4FvAJ8OuY/VOdEwRzFd0MHAC8BTxiZi0yPS8RyZxuUYlIWszsYOBHbJt9/HzgfXe/NGabHwPfAP3dfYaZbSDsBYpty93HxLydZ2bXA5cAV2UY3rcJZgVvFzNr/FVmdhLBLbY/hcsaAf/n7p+F8d4I3Gdm5sHEfL8Exrv7PeH2Y83s20DPMO6yROcUM5HrX9396XDZ5cCPw7imZXheIpIhJTgiksr/C6uZGhH03DwJXBSuOwg4Mkm1U3dgRrJGzex04FfA3gS9PiXhK1MHAc2A5THJBkCTMJZK5ZXJTWgRsBPQmiAx6wXcHdf2m4QJTho+iGsbYLc09xWRLFKCIyKpTAVGAJuBRe6+OWbdDgS3hRKVai9N1qCZHQo8AlwDXAysBk4muP2TqR3CYw5KsG5tzNdb4tZ5zP7ZUHV93N3DZEtDAUQKQAmOiKSy3t0/T7LuHWAoMD8u8Ym1ie17Zo4Avo69TWVmnesY5ztAe2Cru8+tQzufAgOA+2KWHRy3TaJzEpF6Rn9ZiEimbgVaAY+a2SFm1s3Mjg0rmXYOt5kH7Gdm+5hZWzPbEZgN7GlmZ4b7nA8Mq2Ms/wVeIxjgPMTMuprZYWZ2jZkl6tVJZhww3MzONbMeZvY74BC29fQkOycRqWeU4IhIRtx9EUFvzFZgCjCLIOkpD18QjGf5BJgJLAeOCAfh/hn4G8GYleOAq+sYiwMnAC+Gx/yMoNppH7aNhUmnnUeAMcANwLvAfgRVVhtjNtvunOoSu4jkhgU/F0REJBEzmww0cveTCh2LiKRPY3BEREJm1oyg/H0KwYDk04BTwn9FpIioB0dEJGRmTYGnCR4U2BSYA/wxfIqziBQRJTgiIiISORpkLCIiIpGjBEdEREQiRwmOiIiIRI4SHBEREYkcJTgiIiISOf8f+vvyxEnJmggAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f8cc0f6a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 4))\n",
    "plot_decision_boundary(tree_clf_tweaked, X_tweaked, y_tweaked, legend=False)\n",
    "plt.plot([0, 7.5], [0.8, 0.8], \"k-\", linewidth=2)\n",
    "plt.plot([0, 7.5], [1.75, 1.75], \"k--\", linewidth=2)\n",
    "plt.text(1.0, 0.9, \"Depth=0\", fontsize=15)\n",
    "plt.text(1.0, 1.80, \"Depth=1\", fontsize=13)\n",
    "plt.title('Figure 6-8. Sensitivity to training set details')\n",
    "\n",
    "save_fig(\"decision_tree_instability_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.7 Regularization Hyperparameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "决策树对训练数据做出很少的假设（与线性模型假设数据是线性的相反）。如果不受约束，树结构将适应训练数据，非常接近它，并且很可能过拟合它。 这样的模型通常被称为**非参数模型**，不是因为它没有任何参数（它通常有很多），**而是因为参数的数量在训练之前没有确定**，所以模型结构可以自由地贴近数据。 相比之下，诸如线性模型的参数模型具有预定数量的参数，因此其自由度受到限制，从而降低了过拟合的风险（但增加了欠拟合的风险）。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "为避免过拟合训练数据，你需要在训练期间**限制决策树的自由**。 如你所知，这被称为**正则化**。正则化超参数取决于所使用的算法，但通常您至少可以**限制决策树的最大深度**。 在Scikit-Learn中，这由**超参数max_depth**控制（默认值为None，表示无限制）。**减少max_depth将使模型则化，从而降低过拟合的风险**。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**DecisionTreeClassifier类**还有一些其他参数类似地限制了决策树的形状：\n",
    "\n",
    "* min_samples_split（节点在分割之前必须具有的最小样本数），\n",
    "\n",
    "* min_samples_leaf（叶子节点必须具有的最小样本数），\n",
    "\n",
    "* min_weight_fraction_leaf（与min_samples_leaf相同，但表示为加权实例总数的一部分），\n",
    "\n",
    "* max_leaf_nodes（叶子节点的最大数量），\n",
    "\n",
    "* max_features（在每个节点处评估用于拆分的最大特征数）。\n",
    "\n",
    "* 增加超参数 $min_*$  或减少超参数 $max_*$ 将使模型正规化。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "其他算法的工作原理是首先在没有限制的情况下训练决策树，然后修剪（删除）不必要的节点。如果它提供的纯度改善没有统计学意义，子节点都是叶节点的节点被认为是不必要的。标准统计检验，例如$χ^2$ 检验，用于估计改善纯粹是偶然结果的概率（称为零假设）。如果这个概率（称为pvalue）高于给定阈值（通常为5％，由超参数控制），那么该节点被认为是不必要的，并删除其子节点。修剪继续，直到所有不必要的节点都被修剪。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure min_samples_leaf_plot\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f8cbf2dfd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_moons\n",
    "Xm, ym = make_moons(n_samples=100, noise=0.25, random_state=53)\n",
    "\n",
    "deep_tree_clf1 = DecisionTreeClassifier(random_state=42)\n",
    "deep_tree_clf2 = DecisionTreeClassifier(min_samples_leaf=4, random_state=42)\n",
    "deep_tree_clf1.fit(Xm, ym)\n",
    "deep_tree_clf2.fit(Xm, ym)\n",
    "\n",
    "plt.figure(figsize=(11, 4))\n",
    "plt.subplot(121)\n",
    "plot_decision_boundary(deep_tree_clf1, Xm, ym, axes=[-1.5, 2.5, -1, 1.5], iris=False)\n",
    "plt.title(\"No restrictions\", fontsize=16)\n",
    "plt.subplot(122)\n",
    "plot_decision_boundary(deep_tree_clf2, Xm, ym, axes=[-1.5, 2.5, -1, 1.5], iris=False)\n",
    "plt.title(\"min_samples_leaf = {}\".format(deep_tree_clf2.min_samples_leaf), fontsize=14)\n",
    "\n",
    "save_fig(\"min_samples_leaf_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "图6-3(即上图)显示了在moons datasets 上训练的两个决策树（在第5章介绍）。在左侧，使用默认超参数训练决策树（即没有限制），在右侧，使用min_samples_leaf = 4训练决策树。很明显，左边的模型是过拟合的，右边的模型可能会泛化的更好。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "shapes (200,1) and (2,2) not aligned: 1 (dim 1) != 2 (dim 0)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-39-6d2b33d59986>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[0mangle\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpi\u001b[0m \u001b[1;33m/\u001b[0m \u001b[1;36m180\u001b[0m \u001b[1;33m*\u001b[0m \u001b[1;36m20\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[0mrotation_matrix\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcos\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mangle\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m-\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msin\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mangle\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msin\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mangle\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcos\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mangle\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0mXr\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mX\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrotation_matrix\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      4\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mtree_clf_r\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mDecisionTreeClassifier\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrandom_state\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m42\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mValueError\u001b[0m: shapes (200,1) and (2,2) not aligned: 1 (dim 1) != 2 (dim 0)"
     ]
    }
   ],
   "source": [
    "angle = np.pi / 180 * 20\n",
    "rotation_matrix = np.array([[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]])\n",
    "Xr = X.dot(rotation_matrix)\n",
    "\n",
    "tree_clf_r = DecisionTreeClassifier(random_state=42)\n",
    "tree_clf_r.fit(Xr, y)\n",
    "\n",
    "plt.figure(figsize=(8, 3))\n",
    "plot_decision_boundary(tree_clf_r, Xr, y, axes=[0.5, 7.5, -1.0, 1], iris=False)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure sensitivity_to_rotation_plot\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f8cbf4e240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(6)\n",
    "Xs = np.random.rand(100, 2) - 0.5\n",
    "ys = (Xs[:, 0] > 0).astype(np.float32) * 2\n",
    "\n",
    "angle = np.pi / 4\n",
    "rotation_matrix = np.array([[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]])\n",
    "Xsr = Xs.dot(rotation_matrix)\n",
    "\n",
    "tree_clf_s = DecisionTreeClassifier(random_state=42)\n",
    "tree_clf_s.fit(Xs, ys)\n",
    "tree_clf_sr = DecisionTreeClassifier(random_state=42)\n",
    "tree_clf_sr.fit(Xsr, ys)\n",
    "\n",
    "plt.figure(figsize=(11, 4))\n",
    "plt.subplot(121)\n",
    "plot_decision_boundary(tree_clf_s, Xs, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)\n",
    "plt.title('Figure 6-7. Sensitivity to training set rotation')\n",
    "\n",
    "plt.subplot(122)\n",
    "plot_decision_boundary(tree_clf_sr, Xsr, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)\n",
    "plt.title('Figure 6-7. Sensitivity to training set rotation')\n",
    "\n",
    "save_fig(\"sensitivity_to_rotation_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.9 Instability"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**不稳定性**(这部分不是按书上的顺序来的，把最后一小节提前了)\n",
    "\n",
    "希望到现在你确信决策树有很大帮助：它们易于理解和解释，易于使用，功能多样，功能强大。但是他们确实有一些限制。\n",
    "\n",
    "1. 首先，正如你可能已经注意到的，决策树喜欢正交决策边界（所有分裂都垂直于轴），这使得它们**对训练集旋转敏感**。例如，图6-7显示了一个简单的线性可分离数据集：\n",
    "   * 在左侧，决策树可以轻松拆分，\n",
    "   * 在右侧，数据集旋转45°后，决策边界看起来不必要地复杂化。\n",
    "   \n",
    "   尽管两个决策树都完美地拟合训练集，但右侧的模型很可能不会很好地泛化。 限制此问题的一种方法是使用PCA（参见第8章），这通常可以更好地定位训练数据。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. 更一般地说，决策树的主要问题是他们对训练数据中的微小变化非常敏感。例如，如果您只是从鸢尾花训练集（花瓣长4.8厘米，宽1.8厘米）中移除最宽的Iris-Versicolor，并训练一个新的决策树，你可以得到如图6-8所示的模型。如你所见，它与之前的决策树看起来非常不同（图6-2）。由于Scikit-Learn使用的训练算法是随机的，即使在相同的训练数据上也可能得到非常不同的模型（除非你设置了random_state超参数）。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们将在下一章中看到的随机森林可以通过对许多树的预测进行平均来限制这种不稳定性。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.8 Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "决策树还能够执行回归任务。让我们使用Scikit-Learn的**DecisionTreeRegressor类**构建一个回归树，在一个有噪声的二次数据集上训练它，max_depth = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Quadratic training set + noise\n",
    "np.random.seed(42)\n",
    "m = 200\n",
    "X = np.random.rand(m, 1)\n",
    "y = 4 * (X - 0.5) ** 2\n",
    "y = y + np.random.randn(m, 1) / 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DecisionTreeRegressor(criterion='mse', max_depth=2, max_features=None,\n",
       "           max_leaf_nodes=None, min_impurity_decrease=0.0,\n",
       "           min_impurity_split=None, min_samples_leaf=1,\n",
       "           min_samples_split=2, min_weight_fraction_leaf=0.0,\n",
       "           presort=False, random_state=None, splitter='best')"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.tree import DecisionTreeRegressor\n",
    "\n",
    "tree_reg = DecisionTreeRegressor(max_depth=2)\n",
    "tree_reg.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "export_graphviz(\n",
    "        tree_reg1,\n",
    "        out_file=image_path(\"regression_tree.dot\"),\n",
    "        feature_names=[\"x1\"],\n",
    "        rounded=True,\n",
    "        filled=True\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 34,
     "metadata": {
      "image/png": {
       "height": 400,
       "width": 400
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 你的第二个决策树长这样\n",
    "from IPython.display import Image\n",
    "Image(filename=\n",
    "      \"F:/ML/Machine learning/Hands-on machine learning with scikit-learn and tensorflow/images/06_Decision Trees/regression_tree.png\",\n",
    "      width=400,height=400,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "此树看起来与你之前构建的分类树非常相似。**主要区别在于，它不是预测每个节点中的类，而是预测一个值**。例如，假设您要对$x_1 = 0.6$的新实例进行预测。 您从根开始遍历树，最终到达 predicts value = 0.111 的叶节点。 **该预测仅仅是与该叶节点相关联的110个训练实例的平均目标值**。 在这110个实例中，该预测导致均方误差（MSE）等于0.0151。\n",
    "\n",
    "该模型的预测显示在图6-5的左侧。如果设置max_depth = 3，则会获得右侧所示的预测。请注意**每个区域的预测值始终是该区域中实例的平均目标值**。该算法以使得大多数训练实例尽可能接近该预测值的方式分割每个区域。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure tree_regression_plot\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f8cbfeb3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.tree import DecisionTreeRegressor\n",
    "\n",
    "tree_reg1 = DecisionTreeRegressor(random_state=42, max_depth=2)\n",
    "tree_reg2 = DecisionTreeRegressor(random_state=42, max_depth=3)\n",
    "tree_reg1.fit(X, y)\n",
    "tree_reg2.fit(X, y)\n",
    "\n",
    "def plot_regression_predictions(tree_reg, X, y, axes=[0, 1, -0.2, 1], ylabel=\"$y$\"):\n",
    "    x1 = np.linspace(axes[0], axes[1], 500).reshape(-1, 1)\n",
    "    y_pred = tree_reg.predict(x1)\n",
    "    plt.axis(axes)\n",
    "    plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "    if ylabel:\n",
    "        plt.ylabel(ylabel, fontsize=18, rotation=0)\n",
    "    plt.plot(X, y, \"b.\")\n",
    "    plt.plot(x1, y_pred, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
    "\n",
    "plt.figure(figsize=(11, 4))\n",
    "plt.subplot(121)\n",
    "\n",
    "plot_regression_predictions(tree_reg1, X, y)\n",
    "for split, style in ((0.1973, \"k-\"), (0.0917, \"k--\"), (0.7718, \"k--\")):\n",
    "    plt.plot([split, split], [-0.2, 1], style, linewidth=2)\n",
    "plt.text(0.21, 0.65, \"Depth=0\", fontsize=15)\n",
    "plt.text(0.01, 0.2, \"Depth=1\", fontsize=13)\n",
    "plt.text(0.65, 0.8, \"Depth=1\", fontsize=13)\n",
    "plt.legend(loc=\"upper center\", fontsize=18)\n",
    "plt.title(\"max_depth=2\", fontsize=14)\n",
    "\n",
    "plt.subplot(122)\n",
    "\n",
    "plot_regression_predictions(tree_reg2, X, y, ylabel=None)\n",
    "for split, style in ((0.1973, \"k-\"), (0.0917, \"k--\"), (0.7718, \"k--\")):\n",
    "    plt.plot([split, split], [-0.2, 1], style, linewidth=2)\n",
    "for split in (0.0458, 0.1298, 0.2873, 0.9040):\n",
    "    plt.plot([split, split], [-0.2, 1], \"k:\", linewidth=1)\n",
    "plt.text(0.3, 0.5, \"Depth=2\", fontsize=13)\n",
    "plt.title(\"max_depth=3\", fontsize=14)\n",
    "\n",
    "save_fig(\"tree_regression_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "CART算法的工作方式与之前大致相同，除了试图**以最小化杂质的方式分割训练集**之外，它现在尝试**以最小化MSE的方式分割训练集**。 公式6-4显示了算法尝试最小化的成本函数:\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure tree_regression_regularization_plot\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f8cc26b208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tree_reg1 = DecisionTreeRegressor(random_state=42)\n",
    "tree_reg2 = DecisionTreeRegressor(random_state=42, min_samples_leaf=10)\n",
    "tree_reg1.fit(X, y)\n",
    "tree_reg2.fit(X, y)\n",
    "\n",
    "x1 = np.linspace(0, 1, 500).reshape(-1, 1)\n",
    "y_pred1 = tree_reg1.predict(x1)\n",
    "y_pred2 = tree_reg2.predict(x1)\n",
    "\n",
    "plt.figure(figsize=(11, 4))\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.plot(x1, y_pred1, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
    "plt.axis([0, 1, -0.2, 1.1])\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", fontsize=18, rotation=0)\n",
    "plt.legend(loc=\"upper center\", fontsize=18)\n",
    "plt.title(\"No restrictions\", fontsize=14)\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.plot(x1, y_pred2, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
    "plt.axis([0, 1, -0.2, 1.1])\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.title(\"min_samples_leaf={}\".format(tree_reg2.min_samples_leaf), fontsize=14)\n",
    "\n",
    "save_fig(\"tree_regression_regularization_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "就像**分类任务**一样,决策树在处理**回归任务**时容易过拟合。如果没有任何正则化（即使用默认的超参数），您将获得图6-6左侧的预测。\n",
    "显然，这对训练集来说非常严重。只需设置**min_samples_leaf = 10**即可得到更合理的模型，如图6-6右侧所示。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1.to 6.**\n",
    "请移步我的简书[Chapter - 6 Exercise(1- 6)](https://www.jianshu.com/p/8ccb47c541e4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 7.\n",
    "\n",
    "练习：使用moos 数据集训练和微调决策树。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**a.** 使用make_moons(n_samples=10000, noise=0.4).产生一个moons 数据集\n",
    "\n",
    "使用random_state=42 确保笔记本的输出一致："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_moons\n",
    "\n",
    "X, y = make_moons(n_samples=10000, noise=0.4, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**b.** 使用train_test_split()划分训练集和测试集"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**c.** 使用带有**交叉验证的网格搜索**（借助 **GridSearchCV类**）为DecisionTreeClassifier查找好的超参数值。 **提示**：尝试max_leaf_nodes的各种值。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\baideqian\\AppData\\Roaming\\Python\\Python35\\site-packages\\sklearn\\model_selection\\_split.py:1943: FutureWarning: You should specify a value for 'cv' instead of relying on the default value. The default value will change from 3 to 5 in version 0.22.\n",
      "  warnings.warn(CV_WARNING, FutureWarning)\n",
      "[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting 3 folds for each of 294 candidates, totalling 882 fits\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=-1)]: Done  34 tasks      | elapsed:    2.8s\n",
      "[Parallel(n_jobs=-1)]: Done 882 out of 882 | elapsed:    4.3s finished\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "GridSearchCV(cv='warn', error_score='raise-deprecating',\n",
       "       estimator=DecisionTreeClassifier(class_weight=None, criterion='gini', max_depth=None,\n",
       "            max_features=None, max_leaf_nodes=None,\n",
       "            min_impurity_decrease=0.0, min_impurity_split=None,\n",
       "            min_samples_leaf=1, min_samples_split=2,\n",
       "            min_weight_fraction_leaf=0.0, presort=False, random_state=42,\n",
       "            splitter='best'),\n",
       "       fit_params=None, iid='warn', n_jobs=-1,\n",
       "       param_grid={'min_samples_split': [2, 3, 4], 'max_leaf_nodes': [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]},\n",
       "       pre_dispatch='2*n_jobs', refit=True, return_train_score='warn',\n",
       "       scoring=None, verbose=1)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.model_selection import GridSearchCV\n",
    "\n",
    "params = {'max_leaf_nodes': list(range(2, 100)), 'min_samples_split': [2, 3, 4]}\n",
    "grid_search_cv = GridSearchCV(DecisionTreeClassifier(random_state=42), params, n_jobs=-1, verbose=1)\n",
    "\n",
    "grid_search_cv.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DecisionTreeClassifier(class_weight=None, criterion='gini', max_depth=None,\n",
       "            max_features=None, max_leaf_nodes=17,\n",
       "            min_impurity_decrease=0.0, min_impurity_split=None,\n",
       "            min_samples_leaf=1, min_samples_split=2,\n",
       "            min_weight_fraction_leaf=0.0, presort=False, random_state=42,\n",
       "            splitter='best')"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid_search_cv.best_estimator_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**d.** 使用这些超参数在完整的训练集上训练它，并在测试集上测量模型的性能。 你应该得到大约85％到87％的准确率。\n",
    "\n",
    "默认情况下，GridSearchCV会训练整个训练集中找到的最佳模型（您可以通过设置**refit = False**来更改此模型），因此我们不需要再次执行此操作。 我们可以简单地评估模型的准确性："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8695"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "y_pred = grid_search_cv.predict(X_test)\n",
    "accuracy_score(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 8.\n",
    "练习：栽种一个森林"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**a.** 继续上一个练习，生成1,000个训练集子集，每个子集包含随机选择的100个实例。提示：你可以使用Scikit-Learn的ShuffleSplit类。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import ShuffleSplit\n",
    "\n",
    "n_trees = 1000\n",
    "n_instances = 100\n",
    "\n",
    "mini_sets = []\n",
    "\n",
    "rs = ShuffleSplit(n_splits=n_trees, test_size=len(X_train) - n_instances, random_state=42)\n",
    "for mini_train_index, mini_test_index in rs.split(X_train):\n",
    "    X_mini_train = X_train[mini_train_index]\n",
    "    y_mini_train = y_train[mini_train_index]\n",
    "    mini_sets.append((X_mini_train, y_mini_train))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**b.** 使用上面找到的最佳超参数值，在每个子集上训练一个决策树。 在测试集上评估这1,000个决策树。 **由于它们是在较小的集合上训练的**，因此这些决策树可能比第一个决策树表现更差，准确率仅达到约80％。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8054499999999999"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.base import clone\n",
    "\n",
    "forest = [clone(grid_search_cv.best_estimator_) for _ in range(n_trees)]\n",
    "\n",
    "accuracy_scores = []\n",
    "\n",
    "for tree, (X_mini_train, y_mini_train) in zip(forest, mini_sets):\n",
    "    tree.fit(X_mini_train, y_mini_train)\n",
    "    \n",
    "    y_pred = tree.predict(X_test)\n",
    "    accuracy_scores.append(accuracy_score(y_test, y_pred))\n",
    "\n",
    "np.mean(accuracy_scores)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**c.** 下面是见证奇迹的时刻。 对于每个测试集实例，生成1,000个决策树的预测，并仅保留最频繁的预测(你可以使用SciPy的 mode()函数)。\n",
    "这为你提供了对测试集的多数投票预测。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_pred = np.empty([n_trees, len(X_test)], dtype=np.uint8)\n",
    "\n",
    "for tree_index, tree in enumerate(forest):\n",
    "    Y_pred[tree_index] = tree.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import mode\n",
    "\n",
    "y_pred_majority_votes, n_votes = mode(Y_pred, axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**d.** 在测试集上评估这些预测：你应该获得比第一个模型稍高的精度（大约高0.5到1.5％）。 恭喜你已经训练好了了第一个随机森林分类器！"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.872"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(y_test, y_pred_majority_votes.reshape([-1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
